Physics Worksheet Lesson 6 Projectile Motion - Eleanor Roosevelt High ...

Physics Worksheet

Lesson 6: Projectile Motion

Section:

Name:

What is Projectile Motion?

(1) ________________________________________

(2) ________________________________________

1 Based on your observation, what is projectile motion?

(1) ________________________________________

(2) ________________________________________

(3) ________________________________________

(4) ________________________________________

2 Definition of projectile motion:

___________________________________________

___________________________________________

___________________________________________

___________________________________________

___________________________________________

___________________________________________

(3) ________________________________________

(4) ________________________________________

(5) ________________________________________

(6) ________________________________________

6 Formulas for the horizontally launched projectile:

vx = _______________________________________

vy = _______________________________________

dx = _______________________________________

dy = _______________________________________

7 Example: A projectile was fired with initial velocity

10 m/s horizontally from a cliff 19.62 m above the

ground. Calculate the horizontal range of the

projectile.

Trajectory of a Projectile

3 In the absence of gravity, an object in motion will

___________________________________________

__________________________________________.

It will follow the ____________________________.

8 Exercise: A projectile was fired with initial velocity

10 m/s horizontally from a cliff. If the horizontal

range of the projectile is 20 m, calculate the height d

of the cliff.

4 When there is gravity, the trajectory of a projectile

will be a ___________________________________.

The gravity causes the ________________________.

There are no horizontal forces needed to maintain the

__________________________________________.

9 Exercise: A projectile was fired horizontally from a

cliff 19.62 m above the ground. If the horizontal

range of the projectile is 20 m, calculate the initial

velocity v0 of the projectile.

5 Based on the detailed analysis of both the horizontal

and vertical components of the trajectory of the

projectile motion, what are the features of the motion?

Mr. Lin

1

Physics Worksheet

Lesson 6: Projectile Motion

Horizontally Launched Projectile Problems

10 A ball projected horizontally with an initial velocity of 20.

m/s east, off a cliff 100. meters high. [Neglect air

resistance.] (a) During the flight of the ball, what is the

direction of its acceleration? (b) How many seconds does

the ball take to reach the ground?

Section:

Name:

13 Four different balls are thrown horizontally off the top of

four cliffs. In which diagram does the ball have the

shortest time of flight?

11 A tiger leaps horizontally from a 6.5 m high rock with a

speed of 4.0 m/s. How far from the base of the rock will

she land?

14 A pilot flying a constant 215 km/h horizontally in a lowflying helicopter, wants to drop secret documents into his

contact¡¯s open car which is traveling 155 km/h in the

same direction on a level highway 78.0 m below. At what

angle (to the horizontal) should the car be in his sights

when the packet is released?

12 An object is thrown horizontally off a cliff with an initial

velocity of 5.0 meters per second. The object strikes the

ground 3.0 seconds later. (a) What is the vertical speed of

the object as it reaches the ground? (b) How far from the

base of the cliff will the object strike the ground? (c)

What is the horizontal speed of the object 1.0 second

after it is released? [Neglect friction.]

15 Stones are thrown horizontally with the same velocity.

One stone lands twice as far as the other stone. What is

the ratio of the height of the taller building to the height

of the shorter?

Mr. Lin

2

Physics Worksheet

Lesson 6: Projectile Motion

16 Reflection Question: Mathematically prove that the

trajectory of a projectile is actually a parabola (i.e., a

quadratic equation).

Section:

21 A ball was thrown at 30o angle and the speed is 20 m/s.

20 m/s

17 The horizontal and vertical components of velocity for a

projectile on a parabolic path are shown below.

The horizontal component is always the same, and that

only the vertical component changes.

The resultant velocity vector is maximized at _________

Name:

h

30o

d

a)

What¡¯s the minimum speed of the ball in the flight

path? Where will that happen?

b)

How long will the ball travel before hitting the

ground?

c)

What is the maximum high that the ball can reach?

d)

How far will the ball reach horizontally?

e)

What is the final velocity right before hitting the

ground?

f)

If the angle changes to 60o, how far will the ball

reach?

and is a minimum at ____________________________.

The velocity at the top of the path is equal to

_____________________________________________.

18 When a projectile is launching at same speed but at

different angles, the projectile will reach different

vertical heights and travel different horizontal distances

When the launching angle is __________o, the projectile

will reach its maximum horizontal range.

19 The same range can be obtained by two different angles¡ª

¦È and ________________________. The projectile with

smaller angle will remain in the air for a shorter time.

Projectile Launched with an Angle Problems

20 A cannon elevated at an angle of 35o to the horizontal fires

a cannonball and the ball lands at the same height above

the ground from which it was launched.

a) If the ball's time of flight is 10. seconds, what is the

vertical component of its initial velocity?

b)

If the ball lands 7.0 x 102 meters from the cannon 10.

seconds after it was fired, what is the horizontal

component of its initial velocity?

22 A projectile with initial velocity 50 m/s is lunched from

the ground and landed on the ground at the same level.

a) At which angle will the projectile reach the farthest

horizontal distance?

b)

c)

What¡¯s the farthest horizontal distance it can reach?

If the angle of elevation of the cannon is decreased

from 35.o to 30.o, what will happen to the vertical and

horizontal components of the ball's initial velocity?

(increase or decrease?)

Mr. Lin

3

Physics Worksheet

Lesson 6: Projectile Motion

Section:

Name:

23 A cannon fires a projectile at an angle with the horizontal.

The horizontal component of the projectile's initial

velocity is 866 meters per second and its initial vertical

component is 500. meters per second. [Neglect air

resistance.] (a) What is the shape of the path that the

projectile will follow? (b) What is the maximum height

to which the projectile rises? (c) After 5.00 seconds, what

is the vertical component of the projectile's velocity?

24 Projectiles are fired from different angles with the same

initial speed of 14 meters per second. The graph below

shows the range of the projectiles as a function of the

original angle of inclination to the ground, neglecting air

resistance. The graph shows that the

range of the projectiles is A) greatest

for an angle of 90.o B) the same for

angles of 20.o and 80.o C) greatest for

an angle of 45 o D) the same for all

angles.

Mr. Lin

4

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